Series of returns to broad asset classes often possess histories of unequal length and have been subject to smoothing. Estimates of covariances are generally based on the common, although shorter, series length, and covariances for smoothed series are necessarily biased downward. These characteristics pose serious problems that can generate suboptimal and misleading allocations among asset classes. The article discusses elements of the underlying theory in proposing an informationally efficient covariance estimator. The estimator is then compared with conventional covariance estimates in an empirical application. Covariance estimates are found to be sensitive to both truncated estimates involving shorter series and the effects of smoothing.